Dissipative Scalar Field Theory: A Covariant Formulation

Abstract

Caldeira-Leggett model of reservoir is generalized to a reservoir modeled by a continuum of real Klein-Gordon fields, instead of harmonic oscillators. A quantum Langevin type dissipative equation is obtained for the scalar field. The susceptibility of the medium is defined in terms of the reservoir Green's function and the coupling function satisfying causality condition. The connection between the coupling function and the susceptibility of the medium is found to be a Hankel transform from which the coupling function can be determined in terms of the susceptibility of the medium. Noise currents and their fluctuation-dissipation relation are obtained. In a homogeneous medium or reservoir, explicit form of the quantum scalar field, and its large-time limit, are found.

Role of the electromagnetic field in the thermodynamics of the microscopic media

“…The covariant formulation of this work can be done if the medium is modeled by a continuum of Klein-Gordon field [23].…”

Hamiltonian of Mean Force and Dissipative Scalar Field Theory

“…For example in Casimir Physics there are some special geometries where electromagnetic field can be basically considered as two independent scalar fields. Then these scalar fields should be quantized in the presence of a nonhomogeneous magnetodielectric medium where absorption and dispersion properties are taken into account [1,2,3,4]. For the classical case one can model the fluctuating media by a collection of scalar fields and study the fluctuation-induced forces among immersed objects in such a medium [?…”

Quantum Theory of a Strongly-Dissipative Scalar Field

“…Dissipative scalar field theories have an important place in quantum field theory and appear in various problems in physics. Even in quantum mechanics, introducing dissipation in the Hamiltonian of a quantum mechanical system, without invoking to a reservoir or a heat bath, is not a straightforward task and usually leads to inconsistencies in the formulation such as violation of Heisenberg uncertainty principle [1][2][3][4][5]. There are two important approaches to take into account dissipation in quantum theory, namely phenomenological and canonical approach.…”